Problem: $ 256^{-\frac{3}{4}}$
$= \left(\dfrac{1}{256}\right)^{\frac{3}{4}}$ $= \left(\left(\dfrac{1}{256}\right)^{\frac{1}{4}}\right)^{3}$ To simplify $\left(\dfrac{1}{256}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left(? \right)^{4}=\dfrac{1}{256}$ To simplify $\left(\dfrac{1}{256}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left({\dfrac{1}{4}}\right)^{4}=\dfrac{1}{256}$ so $ \left(\dfrac{1}{256}\right)^{\frac{1}{4}}=\dfrac{1}{4}$ So $\left(\dfrac{1}{256}\right)^{\frac{3}{4}}=\left(\left(\dfrac{1}{256}\right)^{\frac{1}{4}}\right)^{3}=\left(\dfrac{1}{4}\right)^{3}$ $= \left(\dfrac{1}{4}\right)\cdot\left(\dfrac{1}{4}\right)\cdot \left(\dfrac{1}{4}\right)$ $= \dfrac{1}{16}\cdot\left(\dfrac{1}{4}\right)$ $= \dfrac{1}{64}$